Problem 7 · 2009 Math Kangaroo
Medium
Number Theory
careful-countingplace-value
A long number is built by writing the number 2009 in a row 2009 times. What is the sum of all the odd digits in this number that are immediately to the left of an even digit?
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Answer: D — 18072
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Hint 1 of 2
Inside the repeated block 2009, which digit sits just before an even digit?
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Hint 2 of 2
Each copy of 2009 contributes the same fixed amount; count how many junctions there are.
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Approach: find the repeating pattern, then multiply
- The string is 2009 2009 2009 … (2009 copies).
- Within one block 2-0-0-9, the only odd digit followed by an even one is the 9 before the next block's 2.
- That happens at each junction between consecutive blocks: 2008 junctions, each adding 9.
- Total = 9 × 2008 = 18072.
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